Rebuking Mitt Romney, President Barack Obama said Tuesday that Americans are not "victims" and that voters want to make sure that their president is "not writing off big chunks of the country."

Obama's remarks came after a secretly taped and newly released video showed the Republican presidential nominee describing "47 percent of the people" as Obama supporters who depend on government and believe they are victims.

"My expectation is that if you want to be president, you have to work for everyone, not just for some," Obama said in a taping of the "Late Show" with David Letterman.

It was Obama's first response to the Romney video, which roiled Romney's campaign and put him on the defensive about his views about nearly half the nation. The president appeared on the TV show before a night of fundraising in New York City.

In the video, taken during a May fundraiser and posted online Monday, Romney said it is not his job "to worry about those people." He was referring to what he called Obama's locked-in supporters who believe they are "entitled to health care, to food, to housing, to you name it."

Romney has since said he made his point inelegantly in trying to describe differing visions for the nation.

"There are not a lot of people out there who think they are victims" or simply entitled, Obama said.

Obama said people understand that the presidential candidates will make mistakes on the campaign trail. He said that includes one he regrets from 2008, when audio from one of his own private fundraisers had him saying that some residents of depressed rural areas get bitter and "cling to guns or religion or antipathy to people who aren't like them."

Having said that, Obama added: "One thing I've learned as president is that you represent the entire country."

The president and Letterman also bantered over lighter subjects, with Obama joking about the Florida pizza restaurant owner who lifted him off the ground in a bear hug last week. "I think he fixed something in my back," Obama said.

The two men exchanged compliments on their appearances.

"You look good," Obama said.

"You haven't seen me naked," Letterman said.

Obama replied: "We're going to keep it that way."

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ater, Obama spoke to about 200 people at a fundraiser at the Waldorf Astoria Hotel. Tickets for the event started at $12,500 per family.

He ended the night at a fundraiser hosted by Beyonce and her husband Jay-Z at the rap mogul's 40/40 Club.

About 100 supporters paid $40,000 per person to attend the party, which was expected to raise about $4 million for Obama's campaign and Democratic Party organizations.